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ENUMERATING PRIME LINKS BY A CANONICAL ORDER

AKIO KAWAUCHI

Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

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and

IKUO TAYAMA

Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

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https://doi.org/10.1142/S0218216506004439Cited by:6 (Source: Crossref)

Abstract

The first author defined a well-order in the set of links by embedding it into a canonical well-ordered set of (integral) lattice points. He also gave elementary transformations among lattice points to enumerate the prime links in terms of lattice points under this order. In this paper, we add some new elementary transformations and explain how to enumerate the prime links. We show a table of the first 443 prime links arising from the lattice points of lengths up to 10 under this order. Our argument enables us to find 7 omissions and 1 overlap in Conway's table of prime links of 10 crossings.

Keywords:

AMSC: 57M25, 57M27

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